Change steepness of an inverse exponential curve…

I’m trying to change the steepness of an inverse exponential curve, whilst keeping (0,1) and (1,0) as fixed points, by changing the variables in the formula y = (a/(x+b))-b. Two examples of correct curves would be a=1, b=~0.618, and a=2, b=1. I need to know how to find b in terms of a, so that I can adjust the curve dynamically with a single input.